We show the consistency of the log-periodogram
regression estimate of the long memory parameter for long
range dependent linear, not necessarily Gaussian, time
series when we make a pooling of periodogram ordinates.
Then, we study the asymptotic behavior of the tapered periodogram
of long range dependent time series for frequencies near
the origin, and we obtain the asymptotic distribution of
the log-periodogram estimate for possibly non-Gaussian
observation when the tapered periodogram is used. For these
results we rely on higher order asymptotic properties of
a vector of periodogram ordinates of the linear innovations.
Finally, we assess the validity of the asymptotic results
for finite samples via Monte Carlo simulation.